5.3: api routes, auth middleware confusion

I'm getting very confused by the differences between routes set-up in web.php and ones in api.php. Also the differences between using $this->middleware('auth') and $this->middleware('auth:api'). Please be patient with me...

Setup:

I have fired up the standard auth setup with php artisan make:auth. registering and logging in with a user works and I end up at /home.

I have a controller called MembersController thats forming a API endpoint, returning JSON. With no auth, this is working as I want it to.

Interestingly, if I add the members resource route to routes/web.php and not routes/api.php, after I log in I do get sent to /home, BUT if I try to go to http://domain.dev/api/v2/members it works, and I see my pretty pretty JSON :)

So... the reason I'm using the api routes is that I want to eventually get auth:api middleware working, and use token auth sent in a header, or a POST var. This is where I've found the docs get rather thin, but it's probably because I have some fundamental understanding missing.